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Ridge-facetings of theoctahedron ship

Possible facets here are the 8 triangles of the comodore itself and the 3 diametral squares. The general naming code here is accordinglyoct-#{3}-#{4}.This gives rise for exactly 4 edge-facetings, without any further restriction. Only 3 of those haven-gonal axial rotation symmetries withn > 2. In fact, just 1 has full octahedral symmetry, 1 has tetrahedral symmetry, and 1 has 4-fold pyramidal symmetry.The fourth possible edge-faceting has 2-fold briquet symmetry only.

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clicking the triple-pictures of the table provides the corresponding VRML preview in this canvas			oct-8-0 = oct	oct-4-3 = thah	oct-4-1 = squippy	oct-4-2 = bobipyr
			octahedral	tetrahedral	4-fold pyramidal	2-fold briquet

Ridge-facetings of thecuboctahedron ship

Possible facets here are the 8 triangles and 6 squares of the comodore itself together with the 4 diametral hexagons.The general naming code here is accordinglyco-#{3}-#{4}-#{6}.This gives rise for exactly 7 edge-facetings, without any further restriction. Only 5 of those haven-gonal axial rotation symmetries withn > 2. In fact, 3 have full octahedral symmetry, and 2 have 3-fold pyramidal symmetry.The other possible edge-facetings have 2-fold briquet symmetry only.

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clicking the triple-pictures of the table provides the corresponding VRML preview in this canvas			co-8-6-0 = co	co-8-0-4 = oho	co-0-6-4 = cho	co-4-3-1 = tricu	co-4-3-3 = gripper	co-4-4-2 = bocuco	co-4-2-2 = ebot
			octahedral			3-fold pyramidal		2-fold briquet